Question

Kim is solving the absolute value inequality |2x – 1| + 3 < 6.

|2x – 1| + 3 < 6
|2x – 1| + 3 – 3 < 6 – 3
|2x – 1| < 3
–3 < 2x – 1 or 2x – 1 < 3
–2 < 2x or 2x < 4
–1 < x or x < 2

Where did Kim go wrong? Explain your reasoning.
A.
Kim should have isolated the absolute value before writing the compound inequality.
B.
Kim should have used –3 > 2x –1 rather than –3 < 2x –1.
C.
Kim should have used "and" instead of "or" in her compound inequality.
D.
Kim should have reversed the inequality symbol when solving 2x > –2.

Answer 1

C. 'Or' means any \(x\) that satisfies at least one of the options works. If \(x=3\), then indeed \(x=3>-1\), but \(x=3\not<2\), so \(x=3\) is not a solution. 'And' means only those values of \(x\) in the interval \(-1<x<2\) are solutions.

Answer 2

ok Thank You so very much :)